For a system of two particles, we often let the potential energy for the force between the particles approach zero as the separation of the particles approaches infinity. If this choice is made, why the potential energy at non-infinite separation is positive if the particles repel one another and negative if they attract?
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For the case where the particles are attracted to each other.
As the particles are attracted to each other they lose potential energy as they get closer (we know they lost potential energy as they have an increase in kinetic energy or they do work). Now we said that the potential energy is zero at infinity, so since the potential energy is lower for non-infinite separation, their potential energy is less than zero, ie negative.
Similarly for the case where the particles repel each other.
As it takes energy to push the particles together it implies that they are at a higher potential energy, and as we said that the potential is zero at infinity, which implies the for non-infinite separation, the potential energy is higher than zero, ie positive.
Hope that helps
Nyra
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The change in potential energy is defined as negative of the work done by conservastive forces. $U_2-U_1=-W_{cons}$
We are taking $U_1=0$ at infinity. If they are brought closer together, a repulsive force would do negative work, thus $U_2$ will be positive, and an attractive force would do positive work, thus $U_2$ would be negative.
dnaik
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